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** Burnside's lemma, a theorem of group theory
Some Related Sentences
** and Burnside's
** and lemma
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** and theorem
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.
** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.
** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.
** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.
** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
** and group
** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).
** Terminology of the British Isles, discusses the sometimes ambiguous or contentious names for parts of the island group
** Marching band, a group of performers that consist of instrumental musicians who generally perform outdoors and incorporate some type of marching ( and possibly other movements ) with their musical performance
** Social Security number with no dashes or spaces followed immediately by " USN ", space, blood group
** Fermentative hydrogen production, the fermentative conversion of organic substrate to biohydrogen manifested by a diverse group of bacteria
** The Pferdestärke PS ( German translation of horsepower ) is a name for a group of similar power measurements used in Germany around the end of the 19th century, all of about one metric horsepower in size.
** Parabolic induction: a method of constructing group representations of a reductive group from representations of its parabolic subgroups.